Question: Which of the following numbers is a multiple of 9? ${79,87,108,110,112}$
Solution: The multiples of $9$ are $9$ $18$ $27$ $36$ ..... In general, any number that leaves no remainder when divided by $9$ is considered a multiple of $9$ We can start by dividing each of our answer choices by $9$ $79 \div 9 = 8\text{ R }7$ $87 \div 9 = 9\text{ R }6$ $108 \div 9 = 12$ $110 \div 9 = 12\text{ R }2$ $112 \div 9 = 12\text{ R }4$ The only answer choice that leaves no remainder after the division is $108$ $ 12$ $9$ $108$ We can check our answer by looking at the prime factorization of both numbers. Notice that the prime factors of $9$ are contained within the prime factors of $108$ $108 = 2\times2\times3\times3\times3 9 = 3\times3$ Therefore the only multiple of $9$ out of our choices is $108$. We can say that $108$ is divisible by $9$.